Precalculus Examples

$\sqrt{16 x} + \sqrt{x^{5}}$

Step 1

Rewrite $16 x$ as ${(2^{2})}^{2} x$ .

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} x} + \sqrt{x^{5}}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{{(2^{2})}^{2} x} + \sqrt{x^{5}}$

$\sqrt{{(2^{2})}^{2} x} + \sqrt{x^{5}}$

Step 2

Pull terms out from under the radical.

$2^{2} \sqrt{x} + \sqrt{x^{5}}$

Step 3

Raise $2$ to the power of $2$ .

$4 \sqrt{x} + \sqrt{x^{5}}$

Step 4

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

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Step 4.1

Factor out $x^{4}$ .

$4 \sqrt{x} + \sqrt{x^{4} x}$

Step 4.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$4 \sqrt{x} + \sqrt{{(x^{2})}^{2} x}$

$4 \sqrt{x} + \sqrt{{(x^{2})}^{2} x}$

Step 5

Pull terms out from under the radical.

$4 \sqrt{x} + x^{2} \sqrt{x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$